Acceleration
ACCELERATION:: The time rate of change in velocity. The SI unit is meters per second2. Acceleration measures the rate that velocity changes, therefore when velocity is constant (if a car is going at a constant 60 mph) then there is no acceleration. Acceleration is a vector quantity because it has both a magnitude and a direction; for example an object moves with an acceleration of 10 m/s2 north. Acceleration is not the same as Velocity. Velocity measures the speed at which an object is moving at a specific time and is measured in METERS per SECOND or m/s. Acceleration is the rate at which that velocity or speed changes and is therefore m/s/s, or m/s2. UNIFORM ACCELERATION Uniform acceleration refers to acceleration that has the same quanitity over a period of time. Imagine a graph that shows TIME on the x-axis and VELOCITY on the y-axis. If the line on this graph is a postive linear line, then the acceleration (slope of the line) is UNIFORM. If a car is driving along a highway and every 3 seconds it increased its speed by a factor of 5 mph. For the amount of time that the car is increasing its speed a thtis rate, the acceleration of the car is uniform. Equations for Uniform Acceleration The equation for the uniform acceleration of an object is... a= ��V/t = (V2-V1)/t V2= V1+ a X t d= V x t + 1/2a X t2 v22= V12+ 2 x a x da=V/t= V Where a= acceleration, V1= initial velocity in meters/ second, V2= final velocity in meters/ second, d= distance in meters and t= time in seconds. *(�� means delta, which means "change in") Uniform Acceleration Question a. The velocity of an car is +47 meters per second at 3.0 seconds and is +65 meters per second at 12.0 seconds. Calculate the acceleration of the car. Solutions to Problems INSTANTANEOUS ACCELERATION Acceleration doesn't always occur at a uniform rate as we studies above. Many times cars and other moving objects don't speed up (or slow down) at a constant rate, sometimes it's faster and sometimes it's slower. This is where we look at instantaneous acceleration. Imagine graph that shows velcity and time, like the one we imagined before. However this time the graph isn't completely linear, it has several linear lines connected to one another. For an example like this, it is necessary to find the acceleration of an object at a specific time, although it is possible to find the average acceleration using the equation change in V/ change in t= V1-V0/ t1-t0 However if you want to find the acceleration at a certain point on a graph like this we have to look at the slope at specific times. The equation to find the slope of a line is as follows change in Y (the axis) / change in X (the axis) This will give you the acceleration at that specific point in time. Equations for Instantaneous Acceleration a=change in V/ change in t slope= change in Y/ change in X Instantaneous Acceleration Question b. What is the acceleration of the object during the time interval t=3 seconds to t=5 seconds? Solutions to Problems FREELY FALLING OBJECTS Freely falling objects refers to the motion of an object falling from rest ner the surface of the Earth (ignore air resistance). When looking at this motion for a varity of objects, it is noted that the velocity of the object increases uniformly at a rate of 9.8 meters/ second2. This number represents ACCELERATION DUE TO GRAVITY. It is an important constant that is used in many different aspects of physics. This number, 9.8m/s2 is denoted as "g" in physics terms. In short, this number is the given acceleration of an object that is given the ability to fall freely, while ignoring the effect of air resistance on the object. Every second that the given obejct falls, another 9.8 m/s2 is added to its speed. NOTE: In this image, the value 9.8 m/s2 is rounded to 10.0 m/s2 Freely Falling Objects Question c. A ball is dropped fromthe roof of a building. What is the velocty of the ball after 4 seconds? How far does the ball fall during this time? Solutions to Problems POSITVE and NEGATIVE ACCELERATION As it is possible to have postive acceleration, it is possible to have negative acceleration as well. We looked at a moving car that was speeding up at a constant acceleration, but what happens when a car slows down? Imagine the postive linear graph described earlier, now think of it with a negative slope. As time passes, the velocity of the car doesn't increase it decreases. This is an example of negative acceleration. Imagine a ball being rolled up a hill. The ball is going to have a negative acceleration at first since it will slow down as it reaches the top of the hill. Then the ball will stop momentarily and then roll down the hill. When the ball rolls down the acceleration will be positive because the ball will speed up as it reached the bottom of the hill. How to Find the Sign of Acceleration Imagine that the moving object is moving on a coordinate plane (you know, a graph). In every case, the coordinate axis should be parallel to the surfce of whatever the object is moving on. When the object is moving in the direction of the positve axis (nomally to the right) then the acceleration of that object is positive. Therefore, if the object is moving in the direction of the negative axis (left) then the acceleration is negative. Postive and Negative Acceleration Question d. If a car is driving at 30 mph and then 10 seconds later is driving at 15 mph, is the acceleration of the car positive or negative? Solutions to Problems ACCELERATION REVIEW QUESTIONS =References= 1. Acceleration 2. Acceleration Due to Gravity 3. Instantanious Acceleration 4. Regents Review Book: Physics The Physical Setting Chapter 2 5. Glencoe Physics: Principles and Problems Chapter 3 and Chapter 5 6. Uniform Acceleration 7. Positive and Negative Acceleration =Resources= 1. Regents Review Book: Physics The Physical Setting 2. Glencoe Physics: Principles and Problems 3. Constant Motion 4. Freely Falling Object 5. Explaination of Acceleration 6. Acceleration Reiview Questions